Talk:Firoozbakht's conjecture

Relation with Cramér–Granville heuristic

I have reverted comments on the relationship of Firoozbakht's conjecture with the Cramér–Granville heuristic as they appear to be original research. Any comments about the degree of belief in the research community in the various conjectures needs to be support by explicit citations to independent reliable sources. Expressions of personal belief in one or the other by individual editors are not acceptable. Deltahedron (talk) 16:17, 4 May 2014 (UTC)

I noticed that since my last edit here these references have been removed:

• 1)

• 2) Daniel Shanks conjectured asymptotic equality of record gaps

I know the second one is not WP:OR and the first is there for just for citing the conjecture. So, why were they removed and should they place back? I am sure better wording can be done, but that is not a reason to remove the cites.

John W. Nicholson (talk) 18:20, 4 May 2014 (UTC)

Added to pick up the references

I reverted what appears to be original research which had deleted several previous citations. Of the two references you cite, one is an Arxiv paper (which is not necessarily a reliable source) and the other is puzzling as it does not appear in the text I reverted. Deltahedron (talk) 18:28, 4 May 2014 (UTC)

An IP user in the 37.254/255 range seems to be engaged in an edit war over this material. I am asking for the page to be restricted to confirmed users only so that we can get a discussion going on this page and consensus on the content. It's not possible to do it with a series of edit summaries. Deltahedron (talk) 21:09, 4 May 2014 (UTC)

Good. But, I think my issue is separate, but relate in the opposite direction -- taking cited material away. I might agree with the reliable source issue with the 1) Arxiv paper if you can show how it is in error with the part talking about the conjecture. The 2) paper does not have this reliable sources issue, but it has been removed by user CRGreathouse. I will agree that it needs some better wording as to what the Shanks conjecture is, but something needs to be said about its relationship to this conjecture. Also, should there be a full article on the Shanks conjecture? John W. Nicholson (talk) 21:48, 4 May 2014 (UTC)

I removed the Arxiv reference as it was being used for original research by synthesis by IP 37.254/255. The preprint does indeed comment on the relationship between Granville's heuristic and Firoozbakht's conjecture, and a reliable source for that would be welcome. However, Arxiv preprints are not reliable sources as such: this has been thrashed out a number of times, see for example, the archives of Wikipedia:Reliable sources/Noticeboard. The Shanks paper from 1964 does not mention the Firoozbakht conjecture. Deltahedron (talk) 07:01, 5 May 2014 (UTC)

Of course not, Shanks paper is from 1964, so it came out before the conjecture here was even founded, but both conjectures "contradicts the Cramér–Granville heuristic" which means that it supports Shanks statement. Also, because there is no representation at Cramér–Granville heuristic, there is no real statement about the Shank conjecture. So, should there be a page? John W. Nicholson (talk) 11:48, 5 May 2014 (UTC)

We need an independent reliable source that compares the various conjectures. Do you know of one? Deltahedron (talk) 11:59, 5 May 2014 (UTC)

www.emis.ams.org/journals/JIS/VOL6/Nicely/nicely2.pdf

I am sure we can find something else which might be more fitting for a Shanks conjecture page, but for this page it looks like both the Cramér–Granville heuristic support and the Shanks heuristic support are use with this page but both are lacking support other than what someone or another will call unreliable sources. Because one of the first published books with the Firoozbakht's conjecture is Paulo Ribenboim 2004 book, I doubt there will be much on it to find connecting the these two more directly than what has already been stated as unreliable sources, so I do not know what is the best thing to do. I do not like this all or nothing bit that the sources are forcing. — Preceding unsigned comment added by Reddwarf2956 (talk • contribs) 16:28, 5 May 2014 (UTC)

The Nyman and Nicely paper does indeed Cramer, Shanks and Granville, but not Firoozbakht, which is what we need here. The point about insisting on independent reliable sources is to verify the material added to the encyclopaedia. Whereof one cannot speak, thereof one must be silent. Deltahedron (talk) 16:41, 5 May 2014 (UTC)

Verification

The text says Using a table of maximal gaps, the inequality can be verified for all primes below 4×10^18. The reference is to a web page Gaps between consecutive primes which does not mention the conjecture and while it might provide the data from which the conjecture might be verified up to this limit (this is not quite clear) there is no assertion that anyone has actually done so. The best I can find is a private communication of Marek Wolf that he has done so up to 3.495×10^16 quoted in Sun, Zhi-Wei (2013). "Conjectures involving arithmetical sequences". In Kanemitsu, Shigeru; Li, Hongze; Liu, Jianya (eds.). Number theory. Arithmetic in Shangri-La. Proceedings of the 6th China-Japan seminar, Shanghai, China, August 15–17, 2011. Series on Number Theory and Its Applications. Vol. 8. Hackensack, NJ: World Scientific. pp. 244–258. ISBN 978-981-4452-44-1. Zbl 1263.11001. Deltahedron (talk) 19:01, 5 May 2014 (UTC)

Before the CRGreathouse edits, that section read "Currently, the largest stated verification was done by using "maximal gaps between consecutive primes less than 4.444 × 10¹² by Firoozbakht. Using a table of maximal gaps and the above gap inequality, the confirmation value can be extended to all primes below 4×10¹⁸." (with the same link to the web page)

This allowed the reader to see how the confirmation was done, and I personally have confirmed it to the 4×10¹⁸ value using the table (worse case was the 64th prime of the table), it is easy. I think the paper you state is an update to the "less than 4.444 × 10¹²" statement or keep the original as the "first" and add this new one as the more one current. What do you feel needs to be done? John W. Nicholson (talk) 21:58, 5 May 2014 (UTC)

Material being removed

I'm not sure why the reddwarf SPA is removing a section from this article. It's properly sourced, has been in the article for a long time, and represents the consensus of the mathematical community. - CRGreathouse (t | c) 12:45, 16 May 2014 (UTC)

You might like to refer to the discussion above, where the issue was, whether the material in question, namely this is relevant, correct and supported the references cited. As I said above, "Any comments about the degree of belief in the research community in the various conjectures needs to be support[ed] by explicit citations to independent reliable sources. Expressions of personal belief in one or the other by individual editors are not acceptable." Let's unpick this material

• The conjecture is believed to be false, as it contradicts the Cramér–Granville heuristic

• Granville, A. (1995), "Harald Cramér and the distribution of prime numbers" (PDF), Scandinavian Actuarial Journal, 1: 12–28
• Granville, Andrew. "Consequences of Legendre's conjecture".
• Granville, Andrew (1995), "Unexpected irregularities in the distribution of prime numbers" (PDF), Proceedings of the International Congress of Mathematicians, 1: pp. 388–399 {{citation}}: |pages= has extra text (help)

None of these references mentions Firoozbakht's conjecture and therefore none of them can be used to support either the proposition that it is believed to be false, or that it contradicts the Cramér–Granville heuristic.

• Pintz refers to this as MCM, the modified Cramér model

• Pintz, János (2007), "Cramér vs. Cramér: On Cramér's probabilistic model for primes", Funct. Approx. Comment. Math., 37 (2): pp. 232–471 {{citation}}: |pages= has extra text (help)

Again, does not mention Firoozbakht's conjecture and hence again cannot be used to support the text.

It might be possible to make an argument that Firoozbakht's conjecture implies Cramér's conjecture and that the latter conjecture with a constant of 1 is inconsistent with a refined form of the conjecture with a constant of 1.1229. This would be merely original research but might be acceptable as obvious to the mathematically sophisticated readership likely for this topic. Even if it were possible, it would still be irrelevant (and so unaccaptable) unless it can be established that Firoozbakht's conjecture implies Carmer with an explicit constant.

However, the assertion "believed to be false" requires an independent reliable source which explicitly addresses that and demonstrates in a scholarly way that the academic consensus is against belief in the conjecture. Where is this claimed consensus published? So far, the references completely fail to address this latter point and so this part of the text completely fails verification. Unverified material which has been repeatedly challenged, as this has, simply cannot be used, and repeatedly inserting it against consensus is Wikipedia:Edit warring. Deltahedron (talk) 16:58, 16 May 2014 (UTC)

This

In the last sentence, it is not clear what "this" is. — Preceding unsigned comment added by 158.58.172.33 (talk) 13:46, 16 May 2014 (UTC)